LAWS OF MOTION for IITJEE

‘Laws of motion’ is a very interesting and important part of the mechanics module of the physics for

IIT and engineering entrance exams. This is the most substantial (like

center of mass) part of mechanics which covers a major portion of JEE

and other engineering entrance exams. Beginners are advised to refer

the study material on Newton’s laws of motion.

Important topic in Laws of motion for IIT JEE

It is a chief topic and can be further divided into important parts like:

Type of forces

Reference frame

Free body diagram (FBD)

Newton’s Laws (First, Second and third)

Rectilinear motion

Circular motion

Friction

Pseudo force and applications

Constraint relation (Dependent relative motion)

Types of forces

Contact forces

Normal force

Tension force

Spring force

Friction force

Push & Pull

Non-contact forces

Gravitational force

Electromagnetic force

Nuclear forces

Weak forces

Frame of reference

It is a conveniently chosen co-ordinate system which describes the position and motion of a body in

space. Any reference frame which is either at rest or in uniform motion is known as inertial frame

of reference and reference frame which is accelerating is known as non-inertial frame of

reference. All Newton’s laws are valid in inertial frame of reference.

Newton’s Laws

First Law (or Law of inertia)

With respect to the inertial frame, a body continues to be in a state of rest or in

the state of uniform motion until we apply an external force on it.

Inertia: The first law of motion describes a property of matter: No body

(dead or living) can change its velocity by itself, without external force acting

on it. This property is known as inertia. Ex: When a car suddenly starts

moving, the passengers in the car are thrown back due to inertia of rest.

Second Law

It states that the rate of change of momentum is directly proportional to the net external force

acting on the body. This change in momentum is in direction of the

resultant force.

Mathematically,

Another form:

Impulse: It is defined as the change in momentum.

Third Law

To every action, there is an equal and opposite reaction. This means that if body A applies a force F⃗

on a body B, then the body B will also exert a force −F⃗ on body A. Ex:

Book kept on a table, walking, swimming, firing from a gun, etc.

Rectilinear Motion:

If we apply a force on a particle along the line of velocity, then direction of momentum (or velocity)

will not change & motion will be along the straight line with change in the magnitude of momentum.

For rectilinear motion:

Net force along any line perpendicular to line of velocity is equal to zero

Net force along line of velocity is equal to 𝑚𝑎

𝑑�⃗�

𝑑𝑡= 𝐹

𝐹 = 𝑚𝑎

Circular Motion

Uniform circular motion

If force is applied perpendicular to the velocity of particle, then only the direction of momentum

will change & magnitude will remain constant and then the body is said to be

in uniform circular motion. For uniform circular motion,

Net force perpendicular to velocity, towards center of circle is given by

Net force along tangent of circle and perpendicular to plane of circle is equal to zero.

Non-uniform circular motion

If applied force is at some acute or obtuse angle with velocity, then motion of particle will be

curvilinear with change in both magnitude and direction.

Net force along center is same as uniform circular motion

Net force along tangent is the product of mass and tangential acceleration

Net force perpendicular to plane of circle is zero

Friction

Whenever one body starts sliding on the surface of the other body, some force gets developed

between them which tries to oppose this relative motion. This is called friction or frictional force.

Static friction

Static friction is frictional force between two contact surfaces when there is no relative motion

between them, though there may be relative motion between them in absence of

friction. Static friction acts:

Parallel to the surface that is perpendicular to the normal

In a direction opposite to relative acceleration in the absence of frictional

force

Note: Limiting friction is the highest value of static friction.

Kinetic friction

Kinetic friction is frictional force between two contact surfaces when there is relative motion

between them in presence or absence of frictional force.

𝐹 = 𝑚𝑎𝑐⃗⃗⃗⃗ = 𝑚𝑣2

𝑅= 𝑚𝜔2𝑅

Magnitude of friction

There is no unique or specific relation for static friction force as it is intelligent and self-

adjustable force which means that it adjusts its value in such a way that the acceleration of

surfaces in contact becomes equal. But there is upper limit of this force beyond which it can’t act

and it is the limiting value of static friction which is mathematically given by

When there is actual relative motion, then kinetic friction is acting and it has a unique value given

by

Note: Normally, 𝜇𝑠 > 𝜇𝑘

Angle of Repose

The angle of inclination up to which a body can continue to be at rest on the inclined surface

without any external force is known as angle of repose. It is dependent on material and nature of

surfaces in contact independent of mass of body.

Angle of Friction

It is the angle between resultant force and normal force to the surface.

Constraint Relation

Constraint relation is a mathematical equation which relates displacement, velocity and acceleration

of two bodies which are in contact or connected by thread, rod and any other thing.

Examples:

Two bodies connected by string

Two rigid bodies in contact

Mass-pulley system

Pseudo Force

Pseudo comes into picture when we describe the motion of a body using non-inertial reference

frame.

The direction of pseudo force is opposite to the direction of real acceleration of non-

inertial reference frame (observer).

The magnitude of pseudo force is the product of mass of body and acceleration of non-

inertial reference frame.

Once we have considered the pseudo force, Newton’s law will give acceleration of particle

relative to that reference frame.

Centrifugal force is a pseudo force acting on a body from a rotating frame.

𝐹𝑠⃗⃗ ⃗(𝑚𝑎𝑥) = 𝜇𝑠𝑁

𝐹𝑘⃗⃗⃗⃗ = 𝜇𝑘𝑁

Is Newton’s Laws of Motion an important part of IIT–JEE preparation?

‘Laws of motion’ is an important part of mechanics which covers 20-25% of JEE physics paper every

year. You really need to master the concepts of this chapter to score high in IIT JEE.

What are the best books for the preparation of Newton’s laws of motion?

Some of the books which are considered to be best for preparation of this section are:

Concepts of Physics by H.C. Verma

Problem in General Physics by I.E. Irodov

Fundamentals of Physics by Halliday, Resnick and Walker

Illustration

Two particles of mass m each are tied at the ends of a light string of length 2a. The whole system

is kept on a frictionless horizontal surface with the string held tight so that each mass is at a

distance ‘a’ from the center P (as shown in the figure). Now, the mid-point of the string is pulled

vertically upwards with a small but constant force F. As a result, the particles move towards each

other on the surface. The magnitude of acceleration, when the separation between them becomes

2x is [IIT-JEE 2007]

Solution:

Some Interesting Facts

When there is static friction between two bodies, then their relative acceleration is zero.

Constraint relations are independent of forces and masses of connected bodies.

Banking of road is done to ensure safe turning even though friction is negligible.

Static fiction value varies from zero to limiting friction value.

Real forces are independent of reference frame

Graphically, impulse is algebraic area of force time curve

We can’t add and subtract forces on two different bodies

Newton’s laws are not valid at atomic or microscopic level.

Tips to study Laws of motion for IIT JEE Preparation

This is the portion of physics where there are chances of committing silly mistakes. You really need

to work on your concepts if you want to excel in this chapter. Here are

some tips which you must follow to score high in this branch:

Do not practice a single problem of laws of motion without drawing a

free body diagram.

Make a different notebook in which you should write important concepts and formulas on daily

basis.

Do not read the same concept from different books as it might lead to confusion. Always stick

to one particular standard text for your concepts.

It is a simple topic but regular practice is essential in order to excel in it.

Always follow the basic root to solve the problem rather than jumping to formulas

Try your level best to solve each problem before seeing its solution.

Practice as many problems as you can from various reference booksas it helps in building up your

confidence and enhance your speed.

Try to solve previous year JEE questions on laws of motion which would really open your mind

and improve your thinking capacity.

Practical Applications of Laws of Motion

Laws of motion do have infinite number of real life applications. Its applications

practically lie in everything that moves. Here are some interesting examples:

It’s used extensively in studying the dynamics of rocket, aircrafts, internal

combustion engine, orbiting satellites, fire arm, etc.

The concepts of the laws of motion are used in many sports like cricket, baseball, football,

javelin throw, car racing, etc.

Third law has various applications in processes like firing from a gun, fight of jet planes and

rockets, walking on sand or ice, rubber ball rebounds from a wall.

Concepts of this chapter are used extensively for various road safety purposes like banking of

roads.

Laws of motion are a substantial part of various industrial applications like machinery, drives,

gears, etc.

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